貝葉斯

首先什么是貝葉斯？

一個例子，現分別有 A、B 兩個容器，在容器 A 里分別有 7 個紅球和 3 個白球，在容器 B 里有 1 個紅球和 9
個白球，現已知從這兩個容器里任意抽出了一個球，且是紅球，問這個紅球是來自容器 A 的概率是多少? 假設已經抽出紅球為事件 B，選中容器 A
為事件 A，則有：P(B) = 8/20，P(A) = 1/2，P(B|A) = 7/10，按照公式，則有：P(A|B) =
(7/10)(1/2) / (8/20) = 0.875

例如：一座別墅在過去的 20 年里一共發生過 2 次被盜，別墅的主人有一條狗，狗平均每周晚上叫 3 次，在盜賊入侵時狗叫的概率被估計為 0.9，問題是：在狗叫的時候發生入侵的概率是多少？
我們假設 A 事件為狗在晚上叫，B 為盜賊入侵，則以天為單位統計，P(A) = 3/7，P(B) = 2/(20365) = 2/7300，P(A|B) = 0.9，按照公式很容易得出結果：P(B|A) = 0.9*(2/7300) / (3/7) = 0.00058

一般公式（解決更復雜的問題）：

樸素的概念：獨立性假設，假設各個特征之間是獨立不相關的

舉例 對應成獨立的時間概率：

貝葉斯模型

• 高斯分布樸素貝葉斯
• 多項式分布樸素貝葉斯
• 伯努利分布樸素貝葉斯

對短信進行二分類—>使用多項式分布樸素貝葉斯實例代碼：

導包加載數據

import warnings warnings.filterwarnings('ignore')import numpy as npimport pandas as pdfrom sklearn.naive_bayes import GaussianNB,BernoulliNB,MultinomialNB sms = pd.read_csv('./SMSSpamCollection.csv',sep = '\t',header = None) sms.columns = ['labels','message'] sms labelsmessage01234...55675568556955705571

ham	Go until jurong point, crazy.. Available only ...
ham	Ok lar... Joking wif u oni...
spam	Free entry in 2 a wkly comp to win FA Cup fina...
ham	U dun say so early hor... U c already then say...
ham	Nah I don't think he goes to usf, he lives aro...
...	...
spam	This is the 2nd time we have tried 2 contact u...
ham	Will ü b going to esplanade fr home?
ham	Pity, * was in mood for that. So...any other s...
ham	The guy did some bitching but I acted like i'd...
ham	Rofl. Its true to its name

5572 rows × 2 columns

measurements = [{'city': 'Dubai', 'temperature': 33.},{'city': 'London', 'temperature': 12.},{'city': 'San Francisco', 'temperature': 18.}, ]from sklearn.feature_extraction import DictVectorizer vec = DictVectorizer()display(vec.fit_transform(measurements).toarray())vec.get_feature_names()

array([[ 1., 0., 0., 33.],
[ 0., 1., 0., 12.],
[ 0., 0., 1., 18.]])

[‘city=Dubai’, ‘city=London’, ‘city=San Francisco’, ‘temperature’]

# 詞頻統計 from sklearn.feature_extraction.text import CountVectorizer X.shape

(5572,)

#Series,一維數據 X = sms['message']y = sms['labels']cv = CountVectorizer() #參數ngram_range() 詞組例如turn on # stop_word 停用詞cv.fit(X)#！！！特征提取特征轉換都是transform#word count:詞頻統計 X_wc = cv.transform(X) X_wc

<5572x8713 sparse matrix of type ‘<class ‘numpy.int64’>’
with 74169 stored elements in Compressed Sparse Row format>

v_ = cv.vocabulary_ v_

{‘go’: 3571,
‘until’: 8084,
‘jurong’: 4374,
‘point’: 5958,
‘crazy’: 2338,
‘available’: 1316,
‘only’: 5571,

v_['its']

4253

##!!!!Serise的用法自帶索引查詢 使用-1需要加iloc X.iloc[-1]

‘Rofl. Its true to its name’

# DataFrame,二維 # 詞頻沒有統計出來，數據格式不對 X = sms[['message']]y = sms['labels']cv = CountVectorizer()cv.fit(X)# word count：詞頻統計 X_wc = cv.transform(X) X_wc

<1x1 sparse matrix of type ‘<class ‘numpy.int64’>’
with 1 stored elements in Compressed Sparse Row format>

使用量化的數據X_wc算法訓練

# X_wc # y from sklearn.model_selection import train_test_split # 稀松矩陣 X_train,X_test,y_train,y_test = train_test_split(X_wc,y,test_size = 0.2) X_train

<4457x8713 sparse matrix of type ‘<class ‘numpy.int64’>’
with 59291 stored elements in Compressed Sparse Row format>

bNB = BernoulliNB()bNB.fit(X_train,y_train)bNB.score(X_test,y_test)

0.9847533632286996

mNB = MultinomialNB()mNB.fit(X_train,y_train)mNB.score(X_test,y_test)

0.9856502242152466

gNB = GaussianNB()gNB.fit(X_train.toarray(),y_train)gNB.score(X_test.toarray(),y_test)

0.9183856502242153

dense_data = X_wc.toarray() dense_data.shape

(5572, 8713)

稀松矩陣存儲大小對比稠密矩陣 ！！

np.save('./dense_data',dense_data) #稠密矩陣330m文件 from scipy import sparse sparse.save_npz('./sparse_data',X_wc) # 稀松矩陣大部分是0，一小部分有對應值 存儲僅需幾百kb X_wc

<5572x8713 sparse matrix of type ‘<class ‘numpy.int64’>’
with 74169 stored elements in Compressed Sparse Row format>

自然語言處理NLP

簡單的自然語言處理：詞頻統計，分類

復雜自然語言處理：語意理解，實時翻譯

import warnings warnings.filterwarnings('ignore') import numpy as npimport pandas as pdimport matplotlib.pyplot as plt %matplotlib inlinefrom sklearn.naive_bayes import GaussianNB,BernoulliNB,MultinomialNB# Count :詞頻統計 # Tfidf:term frequencty inverse documnent frequency(詞頻統計的基礎上，進行了加權) from sklearn.feature_extraction.text import CountVectorizer,TfidfVectorizer,TfidfTransformerfrom sklearn.feature_extraction.text import ENGLISH_STOP_WORDS from jieba import analyse sms = pd.read_csv('./SMSSpamCollection.csv',sep = '\t',header = None) sms.columns = ['target','message'] sms.head() targetmessage01234

ham	Go until jurong point, crazy.. Available only ...
ham	Ok lar... Joking wif u oni...
spam	Free entry in 2 a wkly comp to win FA Cup fina...
ham	U dun say so early hor... U c already then say...
ham	Nah I don't think he goes to usf, he lives aro...

X = sms['message'] y = sms['target'] # 哪些詞區分能力比較強：名字，動詞 ENGLISH_STOP_WORDS # 中文停用詞：我，的，得，了，啊，呢，哼 # 處理中文分詞，jieba分詞 pip install jieba

frozenset({‘a’,
‘about’,
‘above’,
‘across’,
‘after’,
‘afterwards’,
‘again’,

len(ENGLISH_STOP_WORDS)

318

count_word = CountVectorizer() X_cw = count_word.fit_transform(X) v_ = count_word.vocabulary_ len(v_)

8713

count_word = CountVectorizer(stop_words=ENGLISH_STOP_WORDS) X_cw = count_word.fit_transform(X) v_ = count_word.vocabulary_ print(X_cw[10]) len(v_)

(0, 7588) 1
(0, 2299) 1
…

8444

count_word = CountVectorizer(stop_words='english') X_cw = count_word.fit_transform(X) v_ = count_word.vocabulary_ len(v_)

8444

X_dense = X_cw.toarray() X_dense

array([[0, 0, 0, …, 0, 0, 0],
[0, 0, 0, …, 0, 0, 0],
[0, 0, 0, …, 0, 0, 0],
…,
[0, 0, 0, …, 0, 0, 0],
[0, 0, 0, …, 0, 0, 0],
[0, 0, 0, …, 0, 0, 0]], dtype=int64)

(X_dense[:,0] >=1).sum()

10

plt.hist(X_dense[:,0])

(array([5562., 0., 0., 0., 0., 0., 0., 0., 0.,
10.]),
array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ]),
<a list of 10 Patch objects>)

'''Convert a collection of raw documents to a matrix of TF-IDF features.Equivalent to :class:`CountVectorizer` followed by :class:`TfidfTransformer`.''' # TfidfVectorizer == CountVectorizer + TfidfTransformer tf_idf = TfidfVectorizer() X_tf_idf = tf_idf.fit_transform(X) print(X_tf_idf[12])

(0, 4114) 0.09803359946740374
(0, 3373) 0.14023485782692063

…

v_ = tf_idf.vocabulary_ v_

{‘go’: 3571,
‘until’: 8084,
‘jurong’: 4374,
‘point’: 5958,
。。。

v2_ = {} for k,v in v_.items():v2_[v] = k v2_[747]

‘81010’

from sklearn.model_selection import train_test_split X_train,X_test,y_train,y_test = train_test_split(X_tf_idf,y,test_size = 0.2) %%time bNB = BernoulliNB()bNB.fit(X_train,y_train)print(bNB.score(X_test,y_test))

0.97847533632287
Wall time: 19.3 ms

%%time gNB = GaussianNB()gNB.fit(X_train.toarray(),y_train)print(gNB.score(X_test.toarray(),y_test))

0.8914798206278027
Wall time: 1.99 s

測試是否好用？

X_test = ['Pls go ahead with watts. I just wanted to be sure.I check already lido only got 530 show in e afternoon. U finish work already?','Hello, my love. What are you doing?Find out from 30th August. www.areyouunique.co.uk',"Thanx 4 e brownie it's v nice... We tried to contact you re your reply to our offer of 750 mins 150 textand a new video phone call 08002988890 now or reply for free delivery tomorrow",'We tried to contact you re your reply to our offer of a Video Handset? To find out who it is call from a landline 09111032124 . PoBox12n146tf150p','precious things are very few in the world that is the reason there is only one you','for the world you are a person.for me you the whold world']X_test_tf_idf = tf_idf.transform(X_test) X_test_tf_idf

<6x8713 sparse matrix of type ‘<class ‘numpy.float64’>’
with 111 stored elements in Compressed Sparse Row format>

# 第一條短信：兩條正常短信拼接 # 第二條短信：正常和垃圾短信拼接 # 第二條短信：正常和垃圾短信拼接 # 第二條短信：垃圾短信拼接 bNB.predict(X_test_tf_idf)

array([‘ham’, ‘ham’, ‘spam’, ‘spam’, ‘ham’, ‘ham’], dtype=’<U4’)

sklearn 中文本的處理

feature_extract特征‘萃取’

count_word = CountVectorizer(stop_words=ENGLISH_STOP_WORDS,ngram_range=(1,1)) X_cw = count_word.fit_transform(X) v_ = count_word.vocabulary_ print(X_cw[10]) len(v_)

(0, 7588) 1
(0, 2299) 1
(0, 7934) 1

65436

v_= count_word.vocabulary_ d = {} for k,v in v_.items():d[v] = k print(X[0]) print(X_cw[0])

Go until jurong point, crazy… Available only in bugis n great world la e buffet… Cine there got amore wat…
(0, 23208) 1

d[29530]

‘jurong point crazy’

總結

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